Electrical Forces in Simple Harmonic Motion: Finding Frequency and Amplitude

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SUMMARY

The discussion focuses on the conditions under which a point mass carrying charge q, constrained within a frictionless cylinder, exhibits simple harmonic motion (SHM) when influenced by another charge Q. It establishes that SHM occurs if the condition H - kqQ/(mgH) is significantly less than ((kqQ)/(mg))^0.5. The derived frequency of the oscillation is given by the formula 4((mg^3)/(4π^4kqQ)). The relationship between the net force and displacement aligns with Hooke's Law, confirming the oscillatory behavior.

PREREQUISITES
  • Understanding of Coulomb's Law and electric forces
  • Familiarity with simple harmonic motion principles
  • Knowledge of Hooke's Law and its application in oscillatory systems
  • Basic calculus for manipulating equations involving physical constants
NEXT STEPS
  • Explore the derivation of simple harmonic motion equations in electric fields
  • Study the implications of mass and charge on oscillation frequency
  • Investigate the effects of damping in oscillatory systems
  • Learn about the applications of SHM in real-world electrical systems
USEFUL FOR

Physics students, electrical engineers, and anyone interested in the dynamics of charged particles in oscillatory motion will benefit from this discussion.

duke13
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can anyone help with this?
a small point mass m carries a charge q. it is constrained to move vertically inside a narrow, frictionless cylinder. at the bottom of the cylinder is another point mass of Charge Q, same sign as q. the charge q is released from a height H and is observed to fall vertically downwards until it comes to rest for the first time at a vertical height h above Q. the charge then oscillates vertically. show that the motion will be simple harmonic if H-kqQ/(mgH) is much less than ((kqQ)/(mg))^.5. and the frequency will equal 4((mg^3)/(4pi^4kqQ)).



thanks, have been able to show h = kqQ/(Hmg)
 
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SHM will occur if the net force that pulls an object toward an equilibrium position is directly proportional to the displacement from that equilibrium position (such as Hooke's Law, F=-kx).
DOes your equation satisfy this requirement?
 

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